Answer :

Let r and h be the radius and height of the cone respectively.

Then, the volume (V) of the cone is given by:


V=


The surface area (S) of the cone


S = πrl


=





Then,




Now, if


So, when then > 0


Then, by second derivative test, the surface area of the cone is the least when .


So when then h =


Therefore, for a given volume, the right circular cone of the least curved surface has an altitude equal to √2 times the radius of the base.


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